So, I spent some time with Apple customer support. After several of the standard troubleshooting steps for Mystery Problems, they came to the conclusion that there was a driver incompatibility with the Samsung monitor at boot time that was mucking things up, and I would have to just accept booting with the second monitor disconnected, then reconnect it after a successful login.
Samsung does not write monitor drivers for Mac (for whatever reason), which is why customer support figures there was a hangup at booting. But why does OS X recognize the monitor and run it just fine otherwise? Why hang up only at boot time? And why does my 2007 Mac Book Pro running the same version of El Capitan boot just fine with the monitor connected? Does it have something to do with the Thunderbolt/mini-DP-to-DVI connection? I don't know, and I suppose Apple Support doesn't either. 😕
I stumbled upon a kludge, which is this:
1. Boot with the second monitor connected
2. At the "black screen with cursor" hold the power button long enough to put the computer to sleep
3. Wake up the computer with the keyboard or trackpad or whatever
4. Lo and behold the login screen appears.
5. Log in as usual.
6. 🙂
I hope this helps somebody. Someday I will get a more compatible monitor, and it won't be a Samsung.
They make nice TVs, though.